What is the state-of-the-art algorithm for neural style transfer?
So for neural style transfer, using the particular method described in Gatys paper, nobody has done better than using VGG net. This is seemingly due to VGGs inherent stability and inability to learn non-robust features of images. More on this here: https://reiinakano.com/2019/06/21/robust-neural-style-transfer.html
That being said, GANs have had huge success in the field of style transfer, getting much better results than the neural style transfer method described in the paper you mentioned. Cyclegan is one of the best in this respect: https://machinelearningmastery.com/what-is-cyclegan/